There are several methods to describe the nonlinear structure of
the interface of two constant density fluids under potential
theory and the associated nonlinear dynamics has been studied by
many authors [1]}, [2]}, [3]}, [4]}. Layzer [1]}
described the formation of the structure using an expansion near
the tip of the bubble or the spike up to second order in the
transverse coordinates in two dimensional motion and this approach was
extended in Ref. [6]} for Kelvin-Helmholtz instability. It
is well known [7]} that the surface tension reduces the
linear Rayleigh-Taylor Growth rate. The lowering in the growth
rate is seen to increase with increase in the wave number \(k\)  up
to a critical wave number \(k_c=\sqrt{\frac{(\rho _h-\rho _l)g}{T}}\) ,
where \(T\)  denotes surface tension, and \(\rho _h\)  and \(\rho _l\)  are
the densities of the heavier and lighter fluids, respectively. The same effect has been
described by Mikaelian [8]} for Rayleigh–Taylor
instability in finite thickness and Sung-Ik Sohn [9]}
described the effect using the Layzer nonlinear potential model. The nonlinear theory influence of surface tension was elaborately
studied by Pullin [10]} and Garnier et al. [11]}
using numerical methods.
